Problem: What number could replace $k$ below? $\dfrac{1}{3} = \dfrac{k}{9}$
The fraction on the left represents 1 out of 3 slices of a rectangular cake. What if we cut the cake into 9 slices instead? How many slices would result in the same amount of cake? We would need 3 slices. $\dfrac{1}{3} = \dfrac{3}{9}$ and so the answer is $3$ Another way to get the answer is to multiply by $\dfrac{3}{3}$ $\dfrac{3}{3} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{1}{3} \times \dfrac{3}{3} = \dfrac{3}{9} $ so our answer is $3$.